DE4231311A1 - Ascertaining transmission channel pulse response - filtering received test signal to eliminate noise component before evaluation - Google Patents

Abstract

A periodic or aperiodic test signal generated at the transmitter is filtered upon reception at the receiver to eliminate the correlated or uncorrelated noise component. The output of the filter (10) is separated into two parts using a decision algorithm. One of these parts is fed to a further filter (11), a transmission characteristic dependent on the test signal being used to estimate the transmission channel pulse response. Pref. the first filter is followed by a signal separator (14) employing the decision algorithm, coupled to a reduction filter (11) providing a filtered component which is combined with the remaining output of the separation stage. The signal separator may comprise a threshold circuit and an associated control logic (18). USE/ADVANTAGE - Accurate evaluation of pulse response using expanded pulse, e.g. for radar system.

Description

The invention relates to a method according to the preamble of claim 1 and a device for implementation tion of this procedure.

A particularly advantageous application of such a ver driving and such a facility lies with pulse radar systems.

Radar systems can act as impulse response devices estimate. The radar transmitter is transmitting pulse-shaped signal. This runs through a channel and reaches the radar receiver. From the received signal that from the desired signal and from an additive noise signal exists, the impulse response of the channel should be ge be appreciated. The impulse response is determined by the reflective objects from the emitted signal be hit and who scatter this back to the recipient. By interpreting the estimated impulse response therefore information about the location, size and type of get reflective objects.

Achieving high accuracy in impulse response Estimation requires wide bandwidth and high energy sent impulses. High pulse energy is said to be involved the lowest possible peak power of the transmitter output stage  be achieved in order to keep the transmitter effort small. As is known, the requirements mentioned can be met Use of expanded impulses large time-bandwidth- Product.

The system model from which the invention is based is shown in FIG. 1, wherein 1 denotes a transmitter, 2 a transmission channel, 3 an adder and 4 a receiver. All signal forms limited to a measurement bandwidth B bandbe are assigned a sequence of equidistant, time-discrete samples in the equivalent low-pass range. Complex scalar quantities are identified by underlining. Matrices and vectors are shown in bold. The symbols (.) * And (.) ^T mean conjugate complex or transposed.

The expanded send pulse

ª = (ª₁, ª₂... ª _N ) ^T , (1)

the length N at the output of the transmitter 1 according to FIG. 1 passes through the transmission channel 2 with the impulse response

x = ( x ₁, x ₂... x _M ) ^T , (2)

consisting of M distance gates, each of which has a complex reflectivity x _i i = 1. . . M is assigned. With the additive noise

n = ( n ₁, n ₂... n _{M + N-1} ) ^T , (3)

which is fed by the adder 3 , and the Toeplitz matrix

the received signal is calculated

e = ( e ₁, e ₂ ... e _{M + N-1} ) ^T = A x + n , (5)

where A x describes the discrete convolution of the expanded impulse ª with the impulse response x .

The principle of signal processing in the receiver 4, already described in DE-PS 7 68 068 and exclusively used in today's practice, for solving the development problem in determining the impulse response x from the received signal e at an a priori known expanded transmission pulse ª is based on the Filtering of the received signal e with a filter matched to the expanded transmit pulse ª (matched filter). The estimated value is obtained at the output of the signal-matched filter which can be implemented as a digital correlator

_MF =A*^T e = (A*^T A)x +A*^T n      (6)

the channel impulse responsex. To calculate the estimate _MF M · N complex multiplications are to be carried out. At all real expanded impulses ª falsify the Correlation secondary maxima of the autocorrelation function as the elements outside the main diagonals of the matrixA*^T A  in equation (6) the estimate _MF the impulse responsex. Such falsifications cannot be used to fake objectives or to mask the main correlation peak through due to weakly reflective targets Correlation secondary maxima due to highly reflective Lead goals. So you have to focus on the use so far limit the expansion of impulses that are low Correlation secondary maxima are grown. Such a Be Restriction is a hindrance when radar is signal-agile systems are to be realized in which one can build from one select the largest possible class of expanded impulses would like to. Also with specifically mismatched filters (mismatched filter) can remove the harmful correlation benmaxima with a small loss due to the mismatch signal-to-noise ratio (SNR) at the filter output only reduced and thus with the correlation secondary maxima related problems in channel estimation only mitigated become.

An advantageous alternative to signal (mismatched) filtering is the one in the article by T. Felhauer, F. Voigt, FW Baier and A. Mämmelä: "The optimal estimate as an advantageous alternative to the correlation in radar systems with expanded pulses" in the magazine "AEÜ"", Vol. 46, 1992, pages 32 to 37 described unbiased optimal estimate. At the output of an optimal estimator for uncorrelated noise n , equation (4) gives the estimated value

_os = (A*^T A)^-1 A*^T e =x + (A*^T A)^-1 A*^T n      (7)

According to equation (7), the estimated value _os in the real Value of the channel impulse responsex and into an additive Noise component of minimal variance can be separated therefore referred to as the optimal, true-to-expect estimate net. The price for the complete thanks to the expectations The elimination of the correlation secondary maxima is an im Comparison to signal-matched filtering for a large one Class of expanded impulses, low SNR degradation.

The algorithm of the unbiased estimate according to equation (7), in which the received signal e has an M × (M + N-1) estimation matrix

M = [ m _ÿ ] = ( A * ^T A ) ^-1 A * ^T (8)

can be multiplied using a digital correlator according to FIG

L = 2 M + N-1 (9)

time-variant tap coefficientsw _i(k), i = 1. . . L, on Input of L multipliers6 and with L-1 delay elements5 and a summing element7 implemented become. The estimate _os according to equation (7) at the exit8th  of the correlator is obtained when the tap coefficients tenw _i(k) according to the elementsm _ÿ in different Rows of the estimation matrixM change according to equation (8). For Calculation of the estimate _os are thus M · (M + N-1) perform complex multiplications. Is the number M the distance gates of the channel impulse responsex very much greater than the length N of the expanded pulse ª, which in Pulse radar systems is often the case with the an optimal estimate in comparison to the signal-adapted filtering significantly more computing effort connected.  

The invention has for its object a novel Procedure for high-resolution channel estimation for transmissions systems, especially pulse radar systems, with expan impulses based on the expected expectations To create a painting estimate, the computational effort at approximately the same accuracy of the estimated value of the channel impulse response is significantly lower than that of the expected The best estimate according to equation (7).

This task is carried out in a generic method by the in the characterizing part of claim 1 specified features solved.

Appropriate developments of the inventive method rens and an advantageous device for carrying out of the method are in the further claims specified.

The following is a procedure and a setup for cost-effective high-resolution channel estimation relevant invention explained with reference to figures.

Show it

Fig. 1 is an illustration of the system already described model,

FIG. 2 estimator known way to implement a loyal expected Optimal already described,

Fig. 3, the separation of the unbiased optimum contemptuous in decomp matched filter and Nebenmaximal- reduction filter,

Fig. 4, the low-complexity sub-optimal way according to the invention for implementing the expectation true optimal estimation,

Fig. 4a, the autocorrelation function of FIG. 4,

FIG. 4b shows the correlation function of FIG. 4,

Fig. 5 shows a typical channel impulse response x in pulse radar systems,

Fig. 6a, b, c the estimates _MF,_I.,_II,

Fig. 7 filtered ranges of the estimate _II,

Fig. 8 the resulting estimate  as an overlay of the estimate_I. and the post-filtered estimate value_II,

Fig. 9, the signal-to-noise ratio (SNR) Degradation d (L) dependent on the filter length L for a Frank code of length N = 36,

Fig. 10 is a block diagram of a device for the implementing of the method for high-resolution low-cost channel estimation.

In order to obtain a deeper insight into the optimal estimate that is true to expectations and to enable a clear comparison with the signal-adapted filtering, FIG. 3 shows the optimal estimate 9 that is true to expectations in the two function blocks signal-adapted filter 10 and secondary maximum reduction filter 11 .

The matched filter10th first maximizes that Signal-to-interference ratio γ_Max at the exit12th, while the secondary maximum reduction filter11 the disruptive Correlation secondary maxima in the estimate _MF eliminated. Of the Price for this elimination of the correlation secondary maxima is one at the exit13 of the secondary maximum reduction filter11  compared to the maximized signal-to-noise ratio γ_Max  Signal-Stör-Ver reduced by the SNR degradation d ratio γ_a. The optimal estimate, which is true to expectations thus an extension of the theory of conventional  matched filtering. However, since in general all elementsv _ÿ the matrix (A*^T A)^-1 different from zero are, the implementation of the secondary maximum reduction filters11 associated with very great effort. One on Wall-friendly way to implement the secondary maxima reduction filter11 when considering the independent depending on the expanded impulse typical structure of the Ma trix (A*^T A)^-1 obviously, the approximate Toeplitz is structured, d. H. all elements in a respective Diagonals are approximately the same, and the Be sluggish |v _ÿ | of the elementsv _ÿ with increasing distance from of the main diagonals decrease sharply.

If the matrix is approximated by an ideally structured Toeplitz matrix, z. B. the elements of the middle row of the matrix ( A * ^T A ) ^{-1 determine} the elements in the respective diagonals of the ideal Toeplitz-structured matrix, and taking into account only the L elements with the largest amounts around the main diagonal of the matrix ( A * ^T A ) ^-1 , the secondary maximum reduction filter 11 can be suboptimally inexpensive with a digital correlator according to FIG. 2, but with L time-invariant tap coefficients

be implemented. Fig. 4 illustrates this using the example of a Barker code of length N equal to 13 as an expanded transmission pulse ª. In response to a single expanded pulse ª obtained at the output of the matched filter 10, the autocorrelation function shown in Fig. 4a. This autocorrelation function is filtered with a secondary maximum reduction filter 11 , whose L is equal to 50 coefficients selected according to equation (9) from the middle line of the matrix ( A * ^T A ) ^-1 , so that the correlation function shown in FIG Output of this secondary maximum reduction filter 11 results. When calculating the matrix ( A * ^T A ) ^-1 , M was assumed to equal 500 distance gates of the channel impulse response x to be estimated.

In addition to a reduction in the correlation secondary maxima, which also occurs in known similar methods, the correlation function ( FIG. 4b) at the output of a secondary maximum reduction filter 11 specified according to equation (10) has a special feature which is of fundamental importance for the following considerations is. This special feature is the area around the main correlation peak, which always occurs regardless of the selected expanded transmission pulse. The width Δ of this range can be determined in accordance with any expanded pulse of length N solely by the number L of the tap coefficients of the secondary maximum reduction filter 11

Δ = L- (2N-1) + 1 (11)

can be varied. This secondary maximum-free area always occurs when the entire autocorrection function to be filtered ( FIG. 4a) is at the output of the signal-adapted filter 10 within the secondary maximum reduction filter 11 that can be implemented as a digital correlator.

Due to a complex reflectivity x _i , the additive uncorrelated noise n is calculated using the covariance matrix

R _n = E ( n n * ^T ) = σ² _n | (12)

the maximum signal-to-noise ratio at the output of the matched filter 10

Depending on the number L of the tap coefficients w _{i of} the secondary maximum reduction filter 11 , the useful portion is calculated on the basis of the i-th complex reflectivity x _i in the i-th distance gate

The elements of the matrix A * ^T A are _denoted by b _ÿ , i, j = 1. . . M, the elements b _ÿ describing the correlations between the noise values at the output of the signal-matched filter 10 , the variance of the noise component in the i-th distance gate at the output of the secondary maximum reduction filter 11 can be

to calculate. Equation (14) and equation (15) are used to calculate the signal-to-interference ratio in the i-th distance gate at the output of the secondary maximum reduction filter 11

The SNR degradation is calculated depending on the number L of the tap coefficients w _{i of} the secondary maximum reduction filter 11

to

The SNR degradation d (L) according to equation (18) is thus the price that must be paid for the suppression of the correlation ne benmaxima by the secondary maximum reduction filter 11 .

The correlation secondary maxima recognizable in FIG. 4 at the output of the secondary maximum reduction filter 11 arise exclusively during the entry or exit of the autocorrelation function to be filtered ( FIG. 4a) into or out of the secondary maximum reduction filter 11 . In addition to the number L of the tap coefficients of the secondary maximum reduction filter 11, the level of these secondary correlation maxima is also strongly dependent on the choice of the expanded pulse ª, in contrast to the width of the region free of secondary maxima.

For the following algorithm on the high-resolution channel Estimation are the correlation secondary maxima that and leakage of the signal to be filtered into the secondary maxi ma reduction filter11 arise without meaning. Of the The algorithm only uses that regardless of the one selected expanded impulse always occurring side-maximum free Area around the main correlation peak as well as the informa tion based on what can be interpreted as an intermediate estimate Estimate _MF at the output of the matched filter 10th. Furthermore, in pulsed radar systems estimating channel impulse responsesx typically through individual groups of closely neighboring non-vanishing Reflectivities.Fig. 5 shows the amount of one in Pulse radar systems typical channel impulse response, consisting 500 distance gates from M, but only in nine Distance gates on non-vanishing reflectivities to step. These are non-vanishing reflectivities as two groups with four reflectivities each a single reflectivity arranged.

If a Frank multiphase code of length N is equal to 36 as expanded momentum ª is used, so for input-signal-to-noise ratio a_e of 35 dB the in Fig. 6a _MF at the exit of a matched filter10th. Through the annoying corrections  lation secondary maxima become the five smallest reflectivities ten masked so that only the four largest reflections vities can be detected. Furthermore, the Estimate _MF easily in one part _I. in which they interfere the estimation errors are of a purely stochastic nature, see Fig. 6b, and in part _IIin which the disturbing Estimation errors mainly due to correlation secondary maxima are conditional, seeFig. 6c.

The part _I. belongs also to the detected single reflectives act because the correlation secondary maxima due to this Reflectivity below that through the input side Signal-to-noise ratio a_e as well as the process gain p_Max be were the noise levels at the output of the signal-adapted fil ters10th lie and therefore not disturb. Post-filtering from _i is therefore not useful. In contrast, you can by the correlation secondary maxima in the part _II Further Reflectivities must be masked, which is a post-filtering of _II makes sense. The part _II can continue in two Areas are separated that are independent of each other can be filtered. Because these areas are more well known Length as a whole, the entry and exit can be of these ranges into that specified in equation (10) Secondary maximum reduction filter11 be avoided.

If the length is L_x of the range of to be filtered _II  the number L of the tap coefficients of the secondary maxima Re production filter11 to

L = 2 L _x (19)

selected, it can be ensured that the filter range of _II during the L_x Cycle steps for calc of the post-filtered estimate is always completely in within the secondary maximum reduction filter11 is moved, and thus the correlation secondary maxima are eliminated. Fig. 7 shows _II after filtering the individual areas che with the speci. according to equation (10) and equation (19) secondary maximum reduction filter11.Fig. 8 shows the resulting estimate of the channel impulse response as Overlay of the unfiltered area and the post filtered area. It can be seen that all Re flexibility can be clearly detected.

While in part _I. maximum process gain p_Max is present occurs in the filtered areas of _II dependent of the number L of tapes required for post-filtering Coefficients according to equation (18) the SNR degradation d (L) according to equation (18). InFig. 9 is the SNR degradation d (L) for a Frank code of length N equal to 36 over the normalized filter length L / N. With the lengths L_x1  equal to 103 and L_x2 72 can match the corresponding Areas of _II with equation (19) andFig. 9 the SNR Degradations d (L_x1) equal to 1.6 dB and d (L_x2) equal 1.85 dB can be assigned.

The table below is the number of complex Multiplications for the respective estimation algorithms Determination of an estimated value given.

For the example according to FIGS. 6 to 8, the number of complex multiplications for calculating a quasi-secondary maxima-free estimated value could be reduced to 33793 or 12.6% with the inventive method for high-resolution channel estimation from 267500 with optimal expectations. Compared to the signal-adapted filtering, a significantly improved dynamic is achieved through a little additional effort. Since the side maxima free area in the output signal of the side maxima reduction filter 11 occurs independently of the selected expanded pulse, the system designer is no longer restricted to a small class of specially bred expanded pulses with good correlation properties when using the method according to the invention for high-resolution channel estimation. The resulting variety of signal shapes is particularly interesting if a signal-formable pulse radar system is to be implemented.

An advantageous device for implementing the method for cost-effective high-resolution channel estimation according to the invention is described below with reference to FIG. 10.

The receive signale first comes to a in convents tional radar receivers already available suitable filter10th. The estimate _MF at the exit12th of matched filter10th is replaced by one by one Control logic18th controlled threshold switching14 in a part not to be further filtered _I. at the exit16 and in a part falsified by disturbing correlation maxima _II at the exit15 separated. The by the length N of the expanded momentum process gain p_Max of matched filter10th and the input side Signal-to-noise ratio γ_e determine the one for separation necessary noise level at the output12th of the matched signal Filters10th. The parts _I. respectively. _II are first in digital storage19th respectively.17th cached. The individual areas of _II are now sequentially followed up filters. Has a range of _II the length L_x, so be the first 2 · L_x Tap coefficientsw _i the digital one Correlator implementable secondary maximum reduction filter 11 activated according to equation (9). The area to be filtered the length L_x from _II is in the first L_x Memory cells a shift register22 loaded. During the following L_x The area to be filtered is incremented by _II With the one previously through the control logic18th activated Tap Koeffi targetedw _i, i = 1. . . 2L_x, correlated. At the exit20th one Adding element7 this results in that of annoying Kor relationsnebenmaxima freed area of the filtered Part _II. The digital used for post-filtering Correlator (secondary maximum reduction filter11) consists  a shift register22 with 2M memory cells, 2M Multi plice6 to feed the maximum 2M activated Tap coefficientsw _i and the summing element7. The maximal Number of 2M tap coefficients is only activated, if the total estimate at the exit12th of the signalange matched filters10th due to disturbing correlation secondary maxima is adulterated, d. H. if _MF equal _II is. After all Areas of _II have been filtered, is in digital Storage19th by overlaying _I. with the follow-on part _II the resulting estimate  determined and at the exit21 spent.

The maximum 2M tap coefficients required for post-filtering can be calculated a-priori off-line for the expanded transmission pulse used and stored in one of the digital memories 17 or 19 . Since the accuracy of the estimated value at the output 21 of the device according to FIG. 10 depends only to a small extent on the correlation properties of the expanded transmission pulse, the method according to the invention can be used particularly advantageously in signal-formable radar systems, since the system designer chooses the expanded pulses is no longer limited to a class of specially bred waveforms. In a signal-formable radar system, the corresponding 2M tap coefficients must be calculated off-line according to equation (10) for all the expanded pulses used and stored in a digital memory in the receiver. In contrast, if the optimal estimate according to equation (7) is used, a complete estimation matrix M with M · (M + N-1) elements would have to be stored in the receiver for each expanded pulse used. The method according to the invention is thus not only significantly less expensive (see the table already explained above), but also can be implemented much more memory-efficiently than the optimal estimate that is true to expectations.

By a slight modification of the control logic 18 can also be achieved with the device according to FIG. 10 who the that only reflectivities of particular interest render distance gates without systematic errors due to correlation secondary maxima and thus be estimated with the greatest accuracy. Such a modification would be of particular importance in a target tracking radar, where the distance of objects by the tracking algorithm is known a priori in a certain area.

Claims (11)

1. A method for determining the impulse response x (t) of a transmission channel with expanded pulses from a received signal e (t) using knowledge of the periodic or aperiodic test signal a (t) generated in a transmitter, wherein the received signal e (t), the a correlated or uncorrelated interference signal n (t) may be superimposed, in a receiver is first fed to a filter adapted to the test signal a (t), characterized in that the output signal of the signal-adapted filter ( 10 ) by any decision algorithm into a filter to be subsequently filtered Part and a part not to be filtered is separated, the part to be filtered being fed to a further filter ( 11 ), the transmission behavior of which is determined by the test signal a (t) and the width of the part to be filtered and which is independent of the type of the test signal a (t ) eliminates the disturbing correlation maxima in that it is true to expectations Estimated value of the impulse response of the transmission channel is determined within the time range assigned to the part to be filtered. 2. The method according to claim 1, characterized, that by means of the filter matched to the signal Filters the disturbing secondary correlation maxima suboptimally only be suppressed to the extent that they are in the output side Noises disappear. 3. The method according to claim 1 or 2, characterized, that the signal-to-noise ratio of the signal before and / or  after the matched filter, first by coherent and / or incoherent integration is increased by the post to be able to carry out the following separation more easily. 4. The method according to any one of claims 1 to 3, characterized, that the decision algorithm for separating the Signals at the output of the matched filter Control threshold. 5. The method according to any one of claims 1 to 4, characterized, that the received signal in the receiver before further processing processing is digitized first. 6. The method according to any one of the preceding claims, marked by use in a pulse radar receiver. 7. Device for performing the method according to one of the preceding claims, characterized in that the output ( 12 ) of the matched filter ( 10 ) is connected to a signal separation device ( 14 ) influenced by the decision algorithm, that the output for the output signal portion of the signal separation device to be filtered ( 14 ) is connected to a secondary maximum reduction filter ( 11 ), and that the output for the signal portion not to be refiltered and the signal passed through the secondary maximum reduction filter ( 11 ) are combined to form a common output signal. 8. Device according to claim 7, characterized in that the signal separation device is realized by a controllable threshold circuit ( 14 ) in connection with a control logic ( 18 ). 9. Device according to one of claims 7 and 8, characterized in that all filters ( 10 , 11 ) are implemented in analog technology, in particular in the form of electroacoustic tapped delay lines or electroacoustic convolvers. 10. Device according to one of claims 7 and 8, characterized in that all filters ( 10 , 11 ) are implemented by correlators with time variants and / or time-invariant evaluation coefficients in digital technology and one or more digital processors or other digital ones for controlling the process sequence Control units are provided. 11. The device according to claim 10, characterized, that the exit (12th) of the matched filter (10th) With the input of a threshold circuit (14) whose smolder le of a control logic (18th) is controlled, connected is that the threshold circuit has two outputs (16,15) one of which (16) the fil no further interfering signal part ( _I.) to a first input of a also from the control logic (18th) controlled first digital storage (19th) and the other (15) the signal part to be filtered ( _II) at one Input one also from the control logic (18th) controlled, second digital memory (17th) directs that the exit the second digital memory (17th) with one that  Secondary maximum reduction filter (11) educational, digital Correlator is connected which consists of a shift register (22) with 2M memory cells, 2M multipliers (6) to the Feed in of a maximum of 2M through the control logic (18th) before activated tap coefficients (w_i; i = 1. . . 2M) and one Summing element (7) is composed that the output (20th) of the summing element with a second input of the first digital storage (19th) is connected, and that in the first digital storage (19th) the unfiltered ( _I.) and the filtered part ( _TE) of the signal, d. H. his signal parts fed to both inputs, superimposed and a resulting estimate ( ) result, the one at the exit (21) of the first digital memory (19th) is removed.